value of $15,000 in 30 years, at an interest rate of 10%, is $859.63 But that same sum, if paid in 20 years, has a present value of $2,229.65 And if paid in 10 years, its present value is more than twice as great: $5,783.15 The longer the time period before a payment is to be made, the lower its present value The Rate of Interest The present value of a payment of $15,000 to be made in 20 years is $2,229.65 if the interest rate is 10%; it rises to $5,653.34 at an interest rate of 5% The lower the interest rate, the higher the present value of a future payment Table 13.1 "Time, Interest Rates, and Present Value" gives present values of a payment of $15,000 at various interest rates and for various time periods Table 13.1 Time, Interest Rates, and Present Value Present Value of $15,000 Time until payment Interest rate (%) 5 years 10 years 15 years 20 years $11,752.89 $9,208.70 $7,215.26 $5,653.34 10 9,313.82 5,783.15 3,590.88 2,229.65 15 7,457.65 3,707.77 1,843.42 916.50 20 6,028.16 2,422.58 973.58 391.26 The higher the interest rate and the longer the time until payment is made, the lower the present value of a future payment The table below shows the present value of a future payment of $15,000 under different conditions The present value of $15,000 to be paid in five years is $11,752.89 if the interest rate is 5% Its present value is just $391.26 if it is to be paid in 20 years and the interest rate is 20% The concept of present value can also be applied to a series of future payments Suppose you have been promised $1,000 at the end of each of Attributed to Libby Rittenberg and Timothy Tregarthen Saylor URL: http://www.saylor.org/books/ Saylor.org 684